논문KCI 등재
Rational points on Frey elliptic curves y^2=x^3-n^2x
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Abstract
In this work, we study the rational points on eliptic curves of the form y2 = x3 n2x over finite fields in a different way, i.e. using only elementary number theory. We calculate the number of rational point sover Fp modulo 8. We show that here are two possible cases wherep 1or 3 (mod 4). In the former case we find a classication of the number of points, while in the later case, we know that here are p + 1 points on the curve by the supersingular curve theory.
참고문헌 (14)
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관련 논문AI추천
The number of points on elliptic curves $E: y^2 =x^3 +cx$ over $\Bbb F_p$ mod $8$Daeyeoul Kim, Eunhee Lee, Hwasin Park대한수학회 · 대한수학회논문집2003 · 제18권 제1호ON ELLIPTIC CURVES WHOSE 3-TORSION SUBGROUP SPLITS AS μ₃ ⊕ Z/3ZMasaya Yasuda대한수학회 · 대한수학회논문집2012 · 제27권 제3호THE NUMBER OF POINTS ON ELLIPTIC CURVES y2 = x3 + Ax AND y2 = x3 + B3 MOD 24김대열, 전원주대한수학회 · 대한수학회논문집2013 · 제28권 제3호Weierstrass points on hyperelliptic modular curves전대열대한수학회 · 대한수학회논문집2015 · 제30권 제4호Counting points for genus 2 hyperelliptic curves of two special types over finite fieldsG. Y. Sohn장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2014 · 제17권 제1호Integer points on the elliptic curves induced by Diophantine triples박진서대한수학회 · 대한수학회논문집2020 · 제35권 제3호
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